Direct electronic fourier transforms of optical images

ABSTRACT

Method and apparatus for directly converting between optical images and the spatial Fourier transforms of optical images by interacting sound waves and light. Controlled sound waves couple with optical images, and electrical signals may be derived from this coupling which are functions of the spatial Fourier transforms of the entire optical images. In a reverse process, optical images are obtained directly by coupling controlled sound waves with electrical signals which are a function of the spatial Fourier transforms of the optical images and with light.

This is a division of application Ser. No. 493,990, filed Aug. 1, 1974,now U.S. Pat. No. 4,040,091, which is in turn a continuation ofapplication Ser. No. 319,680, now abandoned.

BACKGROUND OF THE INVENTION

The invention relates to converting pictorial information intoelectrical signals and to converting electrical signals into pictorialinformation. More specifically, the invention relates to obtainingFourier transform representations of pictorial information, and forconverting such Fourier transform representations into the correspondingpictorial information. Still more specifically, the invention relates todirectly converting between optical images and the Fourier transformrepresentations of the images.

Electronic processing of pictorial information is an active field, andthere are many devices for converting between pictorial information andelectrical representations thereof. Such prior art devices commonlyrequire arrays of small photosensitive elements. The individual elementsof an array are sensed for changes in a photosensitive parameter when anoptical image is incident on the array. This is explicitly the case indevices such as photodiode mosaics, and is implicitly the case withdevices such as the Vidicon tube, where only a small region of thephotosensitive surface contributes at any one time to the video signalderived from the tube. In such prior art devices, the instantaneousvalue of the derived electrical signal generally represents the lightintensity of a particular portion of an image. Such electrical signalsmay be later processed, such as by analog or digital computers, into aFourier transform representation of the signals and hence of the imagerepresented by the signals. The Fourier transform representation isdesirable, because it allows for more efficient and more versatileelectronic processing of images, such as for improving image resolution,removing noise, providing electronic zoom operations, motion and speeddetection, pattern recognitions, band width compression, etc.

The advantages associated with the use of Fourier transformrepresentations of pictorial information have led to many devices forobtaining such representations. For example, there are programs forutilizing general purpose digital computers to obtain the Fouriertransform representation of electrical signals, and there is a class ofspecial purpose machines called Fast Fourier Transform Computers.Additionally, there is a laser technique for optically obtaining theFourier transform of laser images. This laser technique is based on theobservation that a planar density pattern of coherent light gives riseto its Fourier transform when the pattern is placed in the front focalplane of a lens and the result is observed in the back focal plane (see,for example, Poppelbaum, Computer Hardware theory, McMillan, 1972, pages626 et seq.). It is emphasized that this laser technique is limited tousing coherent light, and cannot be extended to conventional pictorialinformation which, of course, is a non-coherent and polychromaticoptical image.

Because of the desirability of having Fourier transform representationsof pictorial information, there is a need to obtain such representationssimply and efficiently.

It is known that there are relationships between mechanical deformationsof certain materials, optical images incident on the materials andelectrical signals associated with the materials. One example of adevice utilizing such relationships is disclosed in U.S. Pat. No.3,200,824 issued to Yando in 1965. The patent relates to a pick-updevice employing a photoconductive layer in which a light patternprojected on the layer is transformed into a series of output voltagepulses. These output pulses are produced by propagating an elastic waveaccompanied by an electric field along the surface of thephotoconductive layer. These output pulses give some information on therelative one-dimensional distribution of light and dark areas of theimage, but provide no information about the specific light distributionof the light pattern. The pick-up device does not relate to derivingFourier transform representations of images. Another prior art device ofthis type is disclosed in U.S. Pat. No. 3,412,269 issued to Crittenden,Jr. in 1968. The patent discloses a transducer translatingelectromagnetic wave energy to ultrasonic wave energy. The deviceincludes a slab of cadmium sulfide which is exposed to light of aspecific wave length such that alternate dark and light bands areestablished along the acoustic propagation axis of the cadmium sulfide.The dark and light bands are regions of high and low electricalimpedance respectively. The disclosed device does not relate toconversions between optical images and Fourier series or transformrepresentations thereof. Still another prior art device of the type isdisclosed in U.S. Pat. No. 3,649,855 issued to Auld in 1972. Thedisclosed device relates to modulating the conversion of acoustical toelectrical energy by varying a light beam illuminating the convertingmaterial. Again, the disclosed device does not relate to the conversionbetween optical images and Fourier transform representation thereof. Infact, applicants know of no prior art technique for directly obtainingelectrical signals which are spacial Fourier transform representationsof optical images.

SUMMARY OF THE INVENTION

The invention relates to converting between pictorial information andelectrical representations thereof, and relates specifically to directlyconverting between pictorial information and Fourier transformrepresentations thereof. It relies on the discovery that in certainconfigurations of certain materials, there are relationships between theelectrical and mechanical properties of a material that allow derivingelectrical signals representing pictorial information incident on thematerials, and that applying such electrical signals to certainconfigurations of certain materials results in reconstructing theoriginal pictorial information.

Specifically, the invention reflects the discovery of a coupling betweencontrolled sound waves and optical images which allows obtainingelectrical signals that are functions of the spatial Fourier transformsof the optical images, and on the discovery of a coupling between light,controlled sound waves and electrical signals which are a function ofthe spatial Fourier transforms of optical images which allows directlyobtaining the optical images.

In accordance with the invention, such conversions between pictorialinformation and electrical signals representing the pictorialinformation are done directly, by devices which use no spatial scanning,operate at low illumination levels (with visible or infrared, coherentor incoherent light), and require neither high voltages nor highcurrents, such that the driving power for the sound waves may be of theorder of 1 watt. Such devices are inexpensive since they make use ofbulk or surface properties of materials such as common metals,semiconductors or dialectrics, and are rugged. The devices embodying theinvention produce electrical signals representative of the spatialFourier transform of pictorial information incident on the devices.Hence, these electrical signals can be used directly for sophisticatedpictorial information manipulation, which is not possible withelectrical signals which simply represent directly the spatialdistribution of light intensity of an image. For example, the electricalsignals generated by devices embodying the invention can be directly andsimply processed for pattern recognition, as well as for imagemagnification (Zoom) and stabilization. This can be accomplished withoutmachine computation, without camera movement and without lensadjustment. For example, shifting all Fourier transform phases by anamount which is a function of the frequency component and the desiredshift translates the whole picture by a constant amount, multiplying thefrequencies by a constant magnifies the picture, and combining the lasttwo properties yields an electronic zoom capacity. Monitoring andcorrecting for rapid overall changes of phase in the signals generatedby devices constructured in accordance with the invention allowselectronic image stabilization.

One specific example of a device in accordance with the inventioncomprises a medium which has an electrical property that varies as adefined function of pictorial information incident on it and as adefined function of periodic mechanical deformations of the medium. Themedium is subjected to a succession of different periodic mechanicaldeformations, and the electrical property of interest is measured atsuch different periodic deformations to derive a succession ofelectrical signals. These electrical signals serve as an electricalrepresentation of the incident pictorial information. In particular,when the mechanical deformations are caused by vibrating the medium at amultiplicity of different frequencies, each of the electrical signals isderived at a specific vibration frequency and represents the term forthat frequency of a Fourier series representation of the incidentpictorial information. When the mechanical deformation is vibration ofthe medium through a continuous frequency range, the resultingelectrical signal represents the Fourier transform (over finite bounds)of the incident pictorial information.

The fundamental principles of the invention can be illustrated by meansof a device which relies on the coupling between controlled sound wavesand an optical image to generate electrical signals which are functionsof the spatial Fourier transform of the image. In this specification,the term "sound waves" means phonon waves of any frequency, such as fromabout 10 Hz to mega- or gigaHz, and is not limited to frequencies in theaudible range, and the term "controlled sound waves" means sound wavesin which the full wave vector is controlled in terms of magnitude anddirection. The term "Fourier transform" is used generically andincludes, as will become evident below, special cases of themathematical concept of Fourier transforms, such as Fourier series ortruncated Fourier transforms. The term "optical image" is used to meanspatial variations in light intensity, and the term "one-dimensionalimage" is used to mean an optical image in which only the variationsalong one dimension are of interest.

The device which may illustrate the fundamental principles of theinvention comprises a fused quartz substrate and a transducer forgenerating a surface sound wave in the substrate. An intrinsicsemiconductor film, such as CdS, is deposited over a portion of thesubstrate, and a pair of metal contacts are placed over the film but areseparated from each other by a narrow strip of the film. An opticalimage is projected on the exposed strip of film, and a constant voltagedifference is established between the metal contacts across that narrowstrip of film. The transducer is then swept through a frequency range tovibrate the substrate, and hence the semiconductor film thereon at adiscrete or continuous succession of different frequencies. The currentacross the film strip separating the metal contacts is measured atdifferent frequencies. Each measured current value is representative ofthe term, for the particular frequency, of the Fourier transformrepresenting the incident optical image. A number of such narrow stripsof an intrinsic semiconductor film may be arranged next to each other toform a type of a two-dimensional photoconductive device whose resolutionin the direction transverses to the strips' length is limited by thewidths of the strips.

A device for generating an electrical signal representation oftwo-dimension pictorial information comprises a configuration which issimilar to the one-dimensional device, but includes means for generatinga controlled sound wave, which may be obtained for example by nonlinearcoupling of two transducers each operating at its own frequency, withthe result that sound wave beam steering may be accomplished byindependently varying the frequencies of the two transducers.Alternately, a steered sound wave beam may be obtained by using thenormal modes of an acoustical system.

The conversion of pictorial information into an electricalrepresentation thereof may be accomplished alternately by utilizing bulkproperties of degenerate semiconductors and metals, e.g., by making useof strain perturbation of the photoconductivity of such materials. Forexample, a slightly p-type silicon bar which is vibrated at differentfrequencies can be utilized in accordance with the invention to generateelectrical signals which are Fourier transform representations of anoptical image incident on the bar.

There are uses of the devices described above which do not require thereconstruction of the pictorial information represented by theelectrical signals derived thereby. Pattern recognition and informationtransmission are two such uses. If it is required to recreate thepictorial information, two possible ways of doing so are to calculatethe inverse transform of the electrical signals and to display it oncurrently available devices such as cathode ray tubes, or to utilize adirect solid state device constructed in accordance with the invention.

Pictorial information is reconstructed in accordance with the inventionthrough a coupling between light, sound waves and electrical signals.This can be illustrated by a device comprising two parallel polarizingplates having an angle of 90° between their respective planes ofpolarization.

A plate of elasto-optical material (for example, KDP, Plexiglass, orLithium Niobate) is sandwiched between the polarizing plates. Theelasto-optical material has the property of locally changing the angleof polarization of the light passing through it when a mechanical strainis applied to it. The device further includes a transducer coupled withthe elasto-optical plate to produce strain patterns whose amplitude andphase are governed by electrical signals of the type of the signalsderived by the devices described above. Thus, each strain wave in theelasto-optical material plate forms a spatial Fourier component of thepictorial information which is to be reconstructed. The strain rotatesthe polarization locally, thus letting light through the secondpolarizing plate to a detecting device. The system acts like a lightvalve. To add the Fourier component output by this system, use is madeof devices such as an acoustic delay line which adds up and recirculatesthe individual Fourier component sound waves until the entire inversetransform (the acoustic image) is accumulated. Then an electronicshutter or flash tube can illuminate the sound wave complex and theresulting optical image can be focused on a screen.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration used in explaining fundamentalprinciples of the invention.

FIGS. 2, 3 and 4 illustrate obtaining controlled sound waves in asubstrate.

FIG. 5 illustrates a device for obtaining a Fourier transformrepresentation of a one-dimensional optical image.

FIG. 6 illustrates a device similar to FIG. 5, but used to obtain alimited resolution second dimension of an optical image.

FIG. 7 illustrates a different type of a device for obtaining a Fouriertransform representation of a one-dimensional optical image.

FIG. 8 illustrates a device for obtaining a Fourier transformrepresentation of a two-dimensional optical image.

FIG. 9 illustrates another device for obtaining a Fourier transformrepresentation of a two-dimensional optical image.

FIG. 10 illustrates a device for obtaining an optical image from aFourier transform representation of the image.

FIG. 11 illustrates a different form of an output deriving means usefulin connection with the devices shown in FIGS. 5 through 9.

FIG. 12 illustrates the use of devices of the type shown in FIGS. 5through 9 for obtaining a Fourier transform representation of a colorimage.

DETAILED DESCRIPTION

Before describing specific devices constructed and operating accordingto the invention, it may be helpful to define some of the terminologyused in this specification, and to consider certain fundamentalsregarding image formation and the transformation of an optical imageinto electrical signals which are Fourier transform representations ofthe image.

The optical images discussed in this specification are formed byvariations in the intensity of light over a surface which is usually aplanar surface. For simplicity, only a two-dimensional planar surface,in which light intensity may vary both in the X and in the Y directionsis considered. A special case of such planar two-dimensional opticalimages is a one-dimensional image, in which light varies only along asingle dimension, for example, only along the X direction. When Fouriertransforms are discussed in this specification, it should be clear thatit is not the pure mathematical concept of a Fourier transform, but atruncated Fourier transform, where the truncation is due to the factthat the quantities of interest are the Fourier transforms of imagesover finite areas. The mathematical concept of a Fourier transforminvolves an integral taken over indefinite bounds. However, since imagesof finite size are of interest to the subject invention, the integral isover finite bounds, and when the term "Fourier transform" is used, thismeans a transform which is truncated in some way. The term "Fouriertransform" also includes a plurality of Fourier series terms. When theterm "sound wave" is used in this specification, it means a wave ofstrain in a material, where the wave frequency can be any attainablefrequency. It is emphasized that the adjective "sound" is not alimitation to audible frequencies; in fact frequencies of 10 Hz to mega-or gigaHz are useful, and frequencies of 100 kHz to 10 MHz have in factbeen used. The terms "controllable sound waves" and "steered soundwaves" mean sound waves in which the full wave vector (this means themagnitude and direction of the wave vector) can be changed selectively.

Some of the fundamental principles utilized in the subject invention maybe illustrated by referring to FIG. 1 which shows schematically aone-dimensional strip 1 made of a light sensitive medium. Suppose thatthe light incident on an incremental segment dX of the strip 1 producesa change dV_(o) in the potential across the longitudinal ends of theincremental segment dx. Physical constraints require that the actualpotential difference which may be sensed be across a finite length.Suppose that this length has end points a and b. In that case, thepotential difference ΔV_(o) sensed across the points a and b whichdefine the ends of the one-dimensional photosensitive line would be##EQU1## This relationship holds true in the case of the commonphotoconductive sensor. If it is assumed that the change in the voltagedV_(o) is linear in the range of the photon flux density φ(X) of theimage, then the following relationship is true ##EQU2##

A standard approach to image sensing in the prior art is to juxtaposemany identical elements to form an array which allows the separatesensing of each element. The subject invention moves away from thisapproach, and utilizes a single device which generates electricalsignals representing the entire image incident on the device. To explaina fundamental relationship of the subject invention, refer again to thehypothetic one-dimensional photosensitive strip discussed above, andsuppose that the change in voltage across the longitudinal ends of theincremental segment dx is also dependent on a harmonic disturbance ofthe segment, which harmonic disturbance is in the form

    Σ(x,t) = Σ.sub.o e.sup.i(kx-wt)                (e-3)

such that ##EQU3## where k is the propagation constant, w is thetemporal frequency, and is a proportionality constant. Now the voltagedrop across the hypothetical strip defined by the end points a and bbecomes ##EQU4## The first term of the right-hand side in the aboveexpression is simply the potential difference across the segment definedby the end points a and b in the absence of a harmonic disturbance. Thesecond term in the above expression is the term of interest because ittakes the form of the Fourier integral of the photon flux representingthe optical image incident on the hypothetical one-dimensional strip.This second term is small, but is detectable, because it istime-varying, while the first term is not. Calling the second term ofthe above expression ΔV results in the following expressions: ##EQU5##where both the magnitude |ΔV| and phase θ are dependent on the lightintensity φ(X) and on the propagation constant k. The propagationconstant k=k(w) is the dispersion relation for sound waves in thematerial of the strip. It is seen thus that the voltage ΔV has the formof the component of the Fourier transform of the light intensitydistribution φ(X), where φ(X) = 0 outside the end points a and b, at thespatial frequency. The correspondence is then

    F {φ(x)} ⃡ |ΔV| e.sup.iθ(e-7)

and ΔV(w) represents fully the light intensity distribution φ(X) alongthe hypothetical line between the end points a and b. The propagationconstant k is a function of the frequency.

A fundamentally important aspect of the above discussion is that sinceeach Fourier component contains information about the entireone-dimensional strip defined by the end points a and b, the resolutioncapabilities of a detector based on the above discussion is notdetermined by the distance between the end points, but is limited by thehighest spatial frequencies which may be obtainable, and, in anyspecific device, by frequency response limitations of the material andof the sensing electronics. A further fundamentally important aspect isthat a single device, which is many times larger than its resolution,can be used to sense an entire image.

The above discussion indicates why the availability of controlled soundwaves is essential for practicing the subject invention. Since all formsof devices operating according to the invention use some form ofcontrolled sound waves, it may be appropriate to discuss how such wavescan be obtained.

In the case of one-dimensional optical images, controlling the frequencyof vibration of a medium is sufficient. This can be done by vibrating amedium, such as a fused quartz substrate by means of any one of a numberof conventional transducers. For example, referring to FIG. 2, a bar 2of a suitable material, such as fused quartz is vibrated by means of aconventional transducer 3 coupled to the bar 2 by means of a wedge 4 anddriven by a suitable frequency generator 5. Depending on the frequencyof the electrical signal from the source 5 and depending on the relativedimensions, materials and orientation of the bar 2 and transducer 3, asurface sound wave or a bulk sound wave of a particular frequency isinduced in the bar 2. The vibration of the bar 2 may be in a standingwave mode, or alternately the bar 2 may be terminated in an acousticalabsorber 6. The source 5 may be a sweep frequency generator which can beswept, for example, between the frequencies of 100 kHz to 10 MHz todrive the transducer 3. However, the transducer 3 produces an outputonly whenever an odd multiple of half wavelength is equal the length ofthe transducer. Thus, the transducer 3 produces only odd harmonics. Twotransducers of this type may be used, one half as long as the other, togenerate a series of harmonics in which every fourth harmonic ismissing. Using three transducers of the same type, each succeeding beingone-half as long as the preceding one, allows the generation of a seriesof harmonics in which every eight harmonic is missing, etc. Alternately,thin film transducers may be used which offer better control of theoutput characteristics. It is noted that several harmonics of afundamental frequency may be present in the bar 2 at any one time.

A more complex control of a sound wave is needed in the case oftwo-dimensional optical images. If the strain in a medium is a functionof e^(j)(wt - q_(w) ·r), and q_(w) = q_(x) X + q_(y) Y, both q_(x) andq_(y) must be selectively changeable to obtain a sound wave that can becontrolled in the required manner.

One way to obtain the required two-dimensional control of sound waveutilizes the fact that many materials, both crystalline andpolycrystalline, are susceptible to strain amplitudes which result insignificant mixing of the waves due to force terms proportional to thesquare of the strain. If the strain frequencies are less than 100 MHz, aclassical picture of the acoustic waves is adequate.

If two transducers 3a and 3b (see FIG. 3) driven by sources 5a and 5brespectively, are used to generate two sound waves in the same medium 2,namely,

    Σ.sub.1 = Acos (w.sub.1 t-q.sub.x x)

    Σ.sub.2 = Bcos (w.sub.2 t+q.sub.y y)                 (e-8)

and these waves are mixed, the result of nonlinear coupling of the twowaves is a wave which has four components that propagate in the originaldirections established by the transducers 3a and 3b, and a fifth termwhich can be expanded to yield ##EQU6## where V₁ ² q_(x) ² = w₁ ² and V₂² q_(v) ² = W₂ ². Thus the sum and difference frequency terms aresteerable and a controlled sound wave can be so obtained. Both q_(x) andq_(y) can be varied at will by changing the frequencies at which the twotransducers 3a and 3b are driven by the sources 5a and 5b. Themultiplier C₅ involves the third order elastic constant and the productof the original strains AB. Note that the difference term contains the(-q·r) term. The sum term contains the "conjugate" wave vector andshould steer away from a region 7 in FIG. 3, which can be used as animage detecting region. The first four terms of the mixed wave shouldalso propagate away from the image detecting region 7, leaving only thedifference term to couple to a light image that may be projected on theregion 7.

Another solution to the problem of obtaining two-dimensional acousticpatterns is to use the normal modes of an acoustical system. Anelementary example of a solution of this type is illustrated isconnection with FIG. 4. It is assumed that the system illustrated inFIG. 4 works with shear waves of a low-mode nature where there is no zdependence. This is true if ##EQU7## The acoustic waves in this systemare shear waves with displacement V_(i) in the z direction only, andpropagation in the x and y directions. The equation of motion for thedisplacement of such a shear wave is

    V.sub.i = C.sub.s.sup.2 ∇.sup.2 V.sub.i           (e-11)

where C_(s) is the shear velocity of sound in the material of thesubstrate 2 in FIG. 4, and i is the region index. The displacement inthe region 1 shown in FIG. 4 can be expressed as follows: ##EQU8## Bysubstituting the expression (e-12) into the expression (e-11), thefollowing dispersion relation can be obtained for region 1 ##EQU9## Byusing similar expressions for the other regions shown in FIG. 4 andappropriate boundary conditions, it can be shown that B=D=F=O. Thus, aset of normal modes are obtained which can be selected by driving theregions 2 or 3 in FIG. 4 by identical transducers at the same frequency.In order to insure that no degeneracy occurs in the last expression, theratio a/b is chosen to be irrational, for example, b = π/2 a. Theconstraint w<C_(s) π/d can be satisfied for frequencies les than 100 MHzby choosing, for example, d = 0.188 mm, which is a reasonable thicknessof the substrate 2 in FIG. 4. If the dimension a shown in FIG. 4 isapproximately 35 mm, then the expression (e-13) can be solved, for aparticular material, to yield ##EQU10## for all m, n integers.

An exemplary device embodying the subject invention, as applied to thecase of one-dimensional optical images, is shown in FIG. 5. The deviceemploys sound wave modulation of the photoconductance of an intrinsicsemiconductor, and generates electrical signals which are a Fouriertransform representation of a one-dimensional optical image incident ona detecting strip.

Referring to FIG. 5, a substrate 10 which may be a fused quartz bar, hasdeposited on its top surface a film 12 of a photoconductive intrinsicsemiconductor such as CdS. The film 12 is flanked and is partlyoverlapped by two metal contacts 14 and 16 which may be aluminum filmstrips and which are in electrical contact with the semi-conductor film14. The electrical contacts 14 and 16 are spaced from each other by asmall distance to expose a thin strip of the semiconductor film 12 to alight pattern projected from above the substrate 10 by a projector 18.

In one exemplary device, the exposed photodetecting strip of thesemiconductor film 12 is approximately 0.006 inches wide and isapproximately 15mm long, and the semiconductor film 12 is approximately5000 A thick. The semiconductor film in the exemplary device ispolycrystalline CdS which, however, tends to have the C axis of theindividual crystallites aligned perpendicular to the plane of the film12. The film 12 exhibits no net piezoelectric effect in the plane of thefilm. A transducer 20 is acoustically coupled with the top surface ofthe substrate 10 through a Plexiglass wedge 22 and is driven by a sweepfrequency generator 24. This arrangement allows the generation of asurface acoustical wave which propagates along the top surface of thesubstrate 10 from left to right in FIG. 1, i.e., from the transducertowards and through the region under the semiconductor film 12. Theright-hand end of the substrate 10, i.e., the end which islongitudinally opposite the end on which the transducer 20 is mounted iswrapped in acoustical absorbing tape 26 which is for the purpose ofabsorbing substantially without reflection surface sound wavespropagating toward the tape 26 from the transducer 20.

A constant potential difference is established across the electricalcontacts 14 and 16 by means of a constant voltage source 28, and anyvariations in the conductance of the semiconductor 12 are measured bymeasuring the current through a resistor 30 by means of an AC isolatedpreamplifier 32 feeding a phase synchronous detector 34 which alsoreceives as an input an output from the sweep frequency generator 24that carries information about the instantaneous frequency of thegenerator 24. The detector 34 records an electrical signal thatrepresents the instantaneous magnitude and phase of the current acrossthe contacts 14 and 16.

In operation of the device illustrated in FIG. 5, the sweep frequencygenerator 24 is swept from, for example, 100kHz to 10 mHz, to drive thetransducer 20 to generate surface sound waves as discussed in connectionwith FIG. 2. The conductance of the exposed strip of the semiconductorfilm 12, i.e., the strip which is between the contacts 14 and 16, ismodulated both by the light pattern projected on it by means of thelight pattern projector 18 and by the frequency of the surface wavegenerated by the transducer 20. At each sound wave frequency, theconductance measured across the electrical contacts 14 and 16 isrepresentative of the term at that frequency of the Fourier seriesrepresenting the entire one-dimensional light pattern from the projector18.

As a qualitative mathematical discussion of the device of FIG. 5, assumethat the conductance per unit length of the exposed strip of thesemiconductor film 12 can be expressed as follows:

    ΔG = g.sub.D + g.sub.L φ (x) + g.sub.DS Σ + g.sub.LS φ (x)Σ                                                (e-15)

where g_(D) is the dark conductance in the absence of strain, g_(L) φ isthe change in the conductance with light where φ is the photon flux inwatts/m², g_(DS) is the change of dark conductance with strain whereΣ=Σge^(j)(wt-qX) is the strain due to the surface wave generated on thetop surface of the substrate 10 by the transducer 20, and g_(LS) φ(Y)Σis the change in the conductance with light and strain.

The current ΔI per unit length of the exposed strip is then ΔI = ΔGV_(o)where V_(o) is the constant voltage applied across the electricalcontacts 14 and 16 by the constant voltage source 28. The total currentI measured by the preamplifier 32 and the detector 34 across theresistor 30 is then ##EQU11## where X is along the length of the expoledstrip whose longitudinal end point are a and b. The AC component i ofthis current is ##EQU12## However, for the specific material used in theexemplary device in FIG. 1, namely, CdS, the dark to light conductanceratio g_(LS) /g_(DS) is of the order of 300 to 1. Thus, for normal lightintensities, the AC component of the current is approximately ##EQU13##

The expression (e-18) above indicates clearly that the current which ismeasured by the preamplifier 32 and the detector 34 is approximatelyproportional and corresponds to the Fourier transform of the lightintensity pattern projected by means of the projector 18.

In the experimental configuration shown in FIG. 5, a specific devicewhich has been tested has approximately 100 KΩ light resistance andgenerates voltage signals between 30μV and 2mV AC across a 10KΩ resistor30. Since it is desirable to operate with lower impedances than 100KΩseveral devices of the type shown in FIG. 5 may be connected inparallel, with the result being a device of the type shown in FIG. 6.

The device shown in FIG. 6 is similar to that shown in FIG. 5, exceptthat the contacts 14 and 16 of the device in FIG. 5 are replaced by thecontacts 15 and 17 which, as seen in FIG. 3, have interdigitatedcomb-tooth projections 15a and 17a forming six parallel exposed narrowstrips of the semiconductor film 12. A light pattern projected on thedevice shown in FIG. 6 in a manner similar to the projection of a lightpattern on the device shown in FIG. 5 generates in a similar mannerelectrical signals which are substantially the term coefficients of aFourier series representation of the light pattern, and are therefore aFourier transform representation of the light pattern.

A device corresponding generally to the surface effect device shown inFIG. 5, but utilizing bulk properties of certain materials, such asdegenerate semiconductors and metals, is illustrated in FIG. 7. Thedevice shown in FIG. 7 makes use of strain perturbation of thephotoconductivity of a material, and comprises a bar 36 of a materialsuch as a slightly p-type silicon, a light pattern generator 38 forprojecting on the bar 36 a light image which varies only in thedimension along the length of the bar 36, means for vibrating the bar36, means for causing a constant current flow through the bar 36 andmeans for detecting the potential difference across the longitudinalends of the bar 36.

The means for vibrating the bar 36 at selected different frequenciescomprise a sweep frequency generator 40 which is capable of generatingfrequencies from the audio range up to about 100 MHz and which drives atransducer 42 which is acoustically coupled to an acoustic transformerglass pyramid 44 that is in turn acoustically coupled to onelongitudinal end of the bar 36. The opposite longitudinal end of the bar36 is acoustically coupled to a mass of an acoustic absorbing material46 which absorbs substantially without reflection waves propagating fromthe transducer 42 toward the absorbing material 46. A constant currentsource 48 is suitably connected to the opposite longitudinal ends of thebar 36 to establish a constant current flow through the bar 36, and apreamplifier 50 is suitably connected to the longitudinal ends of thebar 36 to measure the instantaneous potential difference therebetween.The output of the preamplifier 50 is connected to a phase synchronousdetector and frequency compensator network 52 which receives as anotherinput an output from the sweep frequency generator 40 carryinginformation identifying the instantaneous frequency of the generator 40.The purpose of the unit 52 becomes apparent from the discussion givenbelow of the mode of operation of the device shown in FIG. 7. The sweepfrequency generator 40, the transducer 42 and their electricalconnections are electrically shielded from the rest of the device shownin FIG. 7 by means of an electrical shielding membrane 54.

In operation, the sweep frequency generator 40 is swept through asuitable range of frequencies to cause thereby bulk wave vibration ofthe bar 36 at a succession of different frequencies defined by thecorresponding harmonics of the transducer 42. At each of thesefrequencies, the potential difference across the longitudinal ends ofthe bar 36 is detected by means of the units 50 and 52, which alsodetect the phase of that voltage signal relative to, for example, thesignal from the generator 40. At each frequency, the voltage detectedacross the ends of the bar 36 corresponds to the term for that frequencyof a Fourier series representation of the one-dimensional light patternprojected on the bar 36 by the light pattern generator 38.

In reality, one does not obtain the Fourer transform of the lightpattern, but rather the transform of the light generated charge carrierdistribution within the measured portion of the bar 36. Thisdistribution is not identical to the light intensity pattern since thecharge carriers tend to defuse away from the place where they aregenerated. This results in a smearing of the light pattern which causesan attenuation of the high frequency Fourier components. This can becorrected to a certain extent by a frequency compensating network whichis included in the phase synchronous detector and frequency compensatornetwork 52. The frequency compensator network simply amplifies the inputsignals which correspond to higher vibrational frequencies. In aspecific experimental device, the bar 36 may be 3500 ohm-cm slightlyp-type silicon having a charge carrier lifetime of about 3ms in adiffusion length of about 5mm. This diffusion length would limitresolution to a few millimeters.

Two-dimensional devices for generating Fourier transform representationsof two-dimensional pictorial information are both more important andmore complicated. Two-dimensional devices constructed and operating inaccordance with the invention may employ essentially the same principlesas the one-dimensional bulk effect and surface effect devices. Thesubstantive difference between the one and two-dimensional devices isthat the two-dimensional devices require a steerable controlled soundwave, so that the second dimension of the pictorial information can beobtained.

One exemplary two-dimensional device utilizes photomissivity and isshown schematically in FIG. 8. The device in FIG. 8 comprises asubstrate 56 of a material such as a fused quartz plate which hasdeposited on one of its large faces a photocathode film 58. Aphotoelectron collector plate 60 is positioned parallel to thephotocathode film 58 and is spaced therefrom by a suitable smalldistance. A constant potential difference is established between thefilm 58 and the collector 60 by means of a constant voltage source 62,and the emission current between the film 58 and the collector 60 ismeasured by means of measuring the potential difference across aresistor 64 by a preamplifier 66 feeding a phase synchronous detector 68which also receives a frequency input from transducers 72. A lightpattern is projected through the substrate 56 onto the photocathode film58 by means of a projector 70. The substrate 56 is vibrated in suitablemodes and at suitable frequencies by means of transducers 72 which aresuitably coupled acoustically to the substrate 56. The device operatesin vacuum.

As a possible qualitative mathematical description of the operation ofthe arrangement shown in FIG. 8, consider the following. Underillumination electrons are emitted from a metal plate in vacuum inaccordance with the Einstein equation

    1/2 mu.sub.max.sup.2 = h.sup.w p - (φ - ev)            (e-19)

where v_(max) is the maximum speed of emitted electrons, w_(p) is thefrequency of light, V is the applied accelerating potential, and φ isthe surface work function. The current density magnitude is

    J = env = eβp(r)v                                     (e-20)

where n is the emitted electron density, p(r) is the photon densityabsorbed, and β is the quantum efficiency of the process. Assuming thatthe temperature is low and that the operation is reasonably close tocut-off, most electrons are emitted with the maximum speed v_(max). Thecurrent density magnitude then becomes

    J = eβp(r) √2/m(h wp-φ+eV)                 (e-21)

when a strain is propagated through the metal of the form

    Σ.sub.ij = Σ.sub.ij.sup.o e.sup.j(wt-q.sbsp.w.sup.·r) (e-22)

where q_(w) is the wave vector related to w by the strain dispersionrelation. This strain provides a local variation in the work function φby varying the Fermi energy. Expanding the work function to first orderin strain, the following expression is obtained: ##EQU14## wheresummation over like indices is assumed throughout. This may be writtenas ##EQU15##

The change in the work function with strain is due to the change of theFermi energy when strained since the vacuum level is fixed. Thus##EQU16## where μ is the Fermi energy. The value of this change can becalculated and it can be shown that this perturbation of φ_(o) is small,but measurable. If the system is arranged so that

    h wp + eV - φ.sub.o >> γφ                    (e-26)

where ##EQU17## The following expression can be calculated for the totalcurrent collected: ##EQU18## where the integral is over the area of thephotoemitter.

From the above expression, it is seen that the component of the currentwhich varies at the strain frequency w is proportional to the q_(w)component of the Fourier transform of the light intensity. Detecting theAC component and scanning in w provides the entire transform. Byincluding a photomultiplier, the parameter β can be manipulated toobtain the required sensitivity.

The principles discussed above are applicable to the arrangement shownin FIG. 8, where electrons are emitted from the photocathode film 58under the effect of the light pattern projected from the projector 70and under the effect of the strain induced by means of the transducers70, and the current is the current through the resistor 64 as measuredby the detector 68.

It should be apparent from the qualitative mathematical discussion abovethat the derivation of the output signal, namely, the current throughthe resistor 64 in FIG. 8, involves integrals whose intergrands containproducts of the intensity distribution of the image projected onto thephotocathode film 58 and the strain deformation of the substrate 56. Ifthe strain is proportional to e^(j)(wt-q_(w).sup.·r), the detectedcurrent signal should be proportional to the two-dimensional Fouriertransform, where q_(w) = q_(x) X + q_(y) y. This condition requiressteering of the acoustical beam causing deformation of the substrate 56.In particular, q_(x) and q_(y) must be changeable essentially by varyingthe frequencies of the electrical signals that may be used to drive thetransducers 72, as discussed earlier in connection with FIGS. 3 and 4.

When the device illustrated in FIG. 8 is used for converting pictorialinformation into an electrical signal representation thereof, it is notnecessary to geometrically separate the various components of the strainwave, since the difference frequency can be detected in a simple mannerand the other signal components can be disregarded. However, in devicesfor converting from electrical signal representations of pictorialinformation into pictorial information, no frequency discrimination ispossible, and any sound wave in the device will modulate the outputpictorial information. It is therefore necessary to find means by whichit would be possible to geometrically separate the various components ofthe strain wave in the substrate. One possible method is illustrated inFIG. 9, and comprises a substrate 56 similar to the substrate 56 in FIG.8 and transducers 74 and 76 which are acoustically coupled to thesubstrate 56 and are driven respectively by sweep frequency generators74a and 76a whose frequencies are independently variable. The strainsinduced in the substrate 56 by means of the transducers 74 and 76 couplenonlinearly (in the manner discussed in connection with FIG. 3) in aregion 56a and couple linearly in a region 56b. The unmixed strain wavesinduced by the transducers 74 and 75 propagate away from a photocathodefilm area 78 which is in the linear mixing region 56b, while thedifference strain wave passes through the photocathode film area 78. Thespecial cases (q_(x),O) and (O,q_(y)) can be obtained by inducing astrain wave in the substrate 56 by means of one of the transducers 80and 82 which are appropriately labelled.

A device equivalent to the two-dimensional device shown in FIG. 8, butrelying on the strain dependence of photoconductance and utilizing thebasic principles discussed in connection with the device of FIG. 5requires a steerable acoustic wave and must take into account the factthat the resistance of a rectangular plate is not proportional to itsarea, that is the product of its dimension, but is proportional ratherto the ratio of its dimension. A one-dimensional device does not presentthis difficulty since we allow no variation in the direction transverseto the current. A two-dimensional device, however, must have provisionsfor taking into account this fact.

Pictorial information which has been converted to the electricalrepresentation discussed above can be recreated either by calculatingthe spatial pattern (inverse transform) and displaying it on currentlyavailable devices such as cathode ray tubes, or by using a direct solidstate projector constructed and operating in accordance with anotheraspect of the invention.

A pictorial information reconstruction system is illustrated in FIG. 10and comprises polarizing plates 86 and 90 and a plate 88 of photoelasticmaterial which is located intermediate the polarizing plates 86 and 90.The planes of polarization of the plates 86 and 90 are at a 90° angle toeach other. For example, the polarization plane of the plate 86 is inthe horizontal direction while the polarization plane of the plate 90 isin the vertical direction. The intermediate plate 88 is of aphotoelastic material, such as for example, KDP or Plexiglass and hasthe property of locally changing the angle of polarization of lightpassing through it when a mechanical strain is applied to it. Thisproperty of elasto-optical materials is well recognized; for example,KDP is used as a light modulator in quantum electronics and Plexiglassis used to demonstrate stress patterns in various mechanical components.Electro-mechanical transducers 92 and 94 are acoustically coupled withthe plate 88 to produce strain patterns similar to the strain patternsdiscussed in connection with FIGS. 3 and 4. The amplitude and phase ofthe strain patterns are governed by electrical signals supplied bysignal generators 92a and 94a whose outputs are in turn governed byelectrical signals of the type derived by the detector 68 in FIG. 8.Thus, each strain wave in the elasto-optical material plate 88 forms aspatial Fourier component of the pictorial information which is to bereconstructed by the arrangement shown in FIG. 10. This strain rotatesthe polarization locally, thus letting light through the polarizationplate 90 which light comes from a collimated light source to the left(in FIG. 10) of the polarization plate 86. The light which istransmitted through the polarization plate 90 can be applied, as asignal, to an acoustic delay line which adds up and recirculates theindividual Fourier component sound waves applied to it until the entireinverse transform (the acoustic image) of a particular optical image isaccumulated. Then an electronic shutter or flash tube can illuminate thesound wave complex and the optical image can focus on a screen. Theplate 88 may be of materials such as lithium niobate.

In connection with the devices illustrated in FIGS. 5 through 9, itshould be noted that in many cases the substrate material vibrates at afundamental frequency and simultaneously vibrates at one or moreharmonics of that fundamental frequency. This can be utilizedadvantageously in simultaneously deriving electrical signalsrepresentative of the Fourier transforms for these several simultaneousfrequencies. Thus, referring to FIG. 11, the block 100 labelled devicerepresents for example the device shown in FIG. 5 and is vibrated bymeans of a source 102. An optical projector 104 projects an opticalimage on the device 100. At each frequency of vibration of the device100, the output signal derived from the device 100 is a Fouriertransform representation of the optical image projected on the device100 by the optical projector 104. However, since the device 100 in factvibrates at a fundamental frequency and one or more detectable harmonicsof that fundamental frequency, it is advantageous to simultaneouslydetect the output at each of these several different frequencies ofvibration of the device 100. Accordingly, the output of the device 100is directed simultaneously to a number of frequency filters, forexample, frequency filters 106a, 106b, and 106c. Each of the frequencyfilters passes only a frequency band corresponding to the fundamentalfrequency or to one of the detectable harmonics of the fundamentalfrequency of vibration of the device 100. Thus, each of the frequencyfilters provides an output which is an electrical signal representativeof the Fourier transform corresponding to the frequency within the bandpass of the filter. These output signals of the filters are recorded ata recorder 108. The filters 106a, 106b, and 106c are controlled by afilter control 110 which receives an input from the source 102 andprovides outputs which determine the band pass frequency of the filters.For example, the filter 106a may be set by means of the filter control110 to pass only electrical signals which correspond to theinstantaneous fundamental frequency of vibration of the device 100, thefilter 106b may be set to pass only electrical signals which correspondto a given harmonic of that instantaneous fundamental frequency ofvibration, and the filter 106c may be set to pass only electricalsignals which correspond to another harmonic of the instantaneousfundamental frequency of vibration of the device 100.

So far, an optical image was considered as represented by the spatialdistribution of light intensity forming the image. However, the devicesdiscussed above may be utilized in a system for obtaining a Fouriertransform representation of a color image, by means of a system of thetype illustrated in FIG. 12. In FIG. 12, an optical image produced by aprojector of the type discussed in connection with FIG. 5 is projectedtoward a device 112, such as a common prism, for separating the opticalimage into the three primary additive colors, blue, green and red. Theresult is three separate optical images, each in only one of the primaryadditive colors. A device of the type shown in FIGS. 5 through 9, forexample a device of the type shown in FIG. 5, is provided for each ofthese three colors. For example, a device 114a is provided for obtainingthe Fourier transform representation of the blue portion of the image, adevice 114b is provided for obtaining the Fourier transformrepresentation of the green portion of the image, and a device 114c isprovided for obtaining the Fourier transform representation of the redimage. Corresponding recording devices 116a, 116b and 116c are providedto record the electrical signal's output by the devices 114a, 114b and114c respectively.

We claim:
 1. A device for generating an electrical signal representationof an optical image comprising:a medium having an electrical propertywhich varies as a function of an optical image formed on the medium andas a function of time and space varying strain disturbances in themedium, said medium being made of a material selected from the groupconsisting of degenerate semiconductors and metals; means for forming anoptical image on the medium; means for causing a plurality of differenttime and space varying strain disturbances in the medium; and means formeasuring said electrical property of the medium at a plurality of saiddifferent strain disturbances in the medium while the image is formed onthe medium to derive a plurality of electrical signals, each signalrepresenting an aspect of the entire image rather than of a point or anelemental area of the image, said measuring means including means forestablishing a constant current across a portion of the medium and meansfor detecting the potential difference across at least a part of saidportion of the medium at a plurality of said different straindisturbances in the medium while the image is formed on the medium.
 2. Adevice as in claim 1 wherein said different strain disturbances in themedium are strain waves of different spatial wavelengths propagating inthe medium.
 3. A device as in claim 1 wherein said strain disturbancesin the medium are bulk strain waves propagating in the medium.
 4. Adevice as in claim 1 wherein the measuring means comprises means forderiving electrical signals each of which is a Fourier transformrepresentation of the image corresponding to a particular straindisturbance in the medium.
 5. A device as in claim 1 wherein the mediumis formed of a continuous, solid, substantially homogeneous materialcapable of propagating strain waves induced therein and having anelectrical property which varies as a Fourier transform function of anoptical image formed on the medium and of strain waves propagating inthe medium.
 6. A device as in claim 5 wherein the medium comprisesessentially a bar of silicon material.
 7. A device as in claim 1 whereinthe means for measuring the electrical property comprises means forderiving electrical signals each of which represents a selectedcomponent of a Fourier transform representation of a single dimension ofthe optical image.
 8. A device as in claim 1 wherein the measuring meansincludes means for measuring the magnitude of said electrical propertyof the medium and the phase of said electrical property relative to thestrain disturbances present in the medium to thereby derive electricalsignals representing both the magnitude and the phase of said property,said electrical signals representing the optical image.
 9. A device asin claim 1 wherein the means for causing strain disturbances comprisemeans for causing a plurality of strain waves of different spatialwavelengths to be concurrently present in the medium and the measuringmeans include means for deriving an electrical signal corresponding toeach of the concurrently present strain waves, said electrical signalrepresenting a Fourier transform representation of the imagecorresponding to said concurrently present strain waves.
 10. A devicefor generating an electrical signal representation of an optical imagecomprising:a medium having an electrical property which varies as afunction of an optical image formed on the medium and as a function ofstrain disturbances present in the medium; means for forming an opticalimage on the medium; means for causing a plurality of strain waves ofdifferent spatial wavelengths to be concurrently present in the medium;and means for measuring the electrical property of the medium at each ofsaid plurality of different strain waves to derive a correspondingplurality of electrical signals each of which represents an aspect ofthe entire optical image rather than of a point or an elemental area ofthe image.
 11. A device as in the claim 10 wherein each of said strainwaves in the medium is a bulk strain wave.
 12. A device as in claim 10wherein the measuring means includes means for deriving electricalsignals each of which represents a Fourier transform component of theoptical image.
 13. A device as in claim 10 wherein the measuring meansincludes means for measuring the magnitude of the electrical property ofthe medium corresponding to each of said strain waves and the phase ofthe electrical property of the medium corresponding to each of saidstrain waves and relative to the phase of the corresponding strain wave.14. A method of deriving an electrical signal representation of anoptical image comprising the steps of:forming an optical image on amedium having an electrical property which varies as a function of theoptical image formed on it and as a function of strain disturbancespresent in it; causing a plurality of different strain disturbances inthe medium; and measuring the electrical property of the medium at aplurality of said different strain disturbances in the medium to derivea plurality of electrical signals each corresponding to a differentstrain disturbance and each representing the entire optical image formedon the medium, said measuring means including means for maintaining aconstant current through a selected portion of the medium and forderiving said electrical signals by measuring the potential differenceacross said selected portion of the medium.
 15. A method as in claim 14wherein the step of causing the strain disturbances comprises causingbulk strain waves propagating through the medium.
 16. A method as inclaim 14 wherein the measuring step comprises measuring the electricalproperty to derive electrical signals each of which is a Fourierrepresentation component corresponding to a different strain disturbancein the medium.
 17. A method as in claim 14 wherein the measuring stepcomprises measuring the magnitude of the electrical propertycorresponding to each of the different strain waves and measuring thephase of the electrical property corresponding to each different straindisturbance and relative to the phase of the corresponding straindisturbance.